It is not essential to make up for missed fasts consecutively. If he does that, it is better, but if he does not there is nothing wrong with that.

The majority of scholars said that it is not permissible to fast on the Days of Tashriq whether it is an optional fast, making up a missed fast or fasting in fulfillment of a vow. So, the fasts that you observed on the Days of Tashriq to make up for missed Ramadan fasts, are not valid, and you must repeat them.